In this function, the expression, (interactive "p"), is a list of
two elements. The "p" tells Emacs to pass the prefix argument to
the function and use its value for the argument of the function.

The argument will be a number. This means that the symbol
number will be bound to a number in the line:

(message "The result is %d" (* 7 number))

For example, if your prefix argument is 5, the Lisp interpreter will
evaluate the line as if it were:

(message "The result is %d" (* 7 5))

(If you are reading this in GNU Emacs, you can evaluate this expression
yourself.) First, the interpreter will evaluate the inner list, which
is (* 7 5). This returns a value of 35. Next, it
will evaluate the outer list, passing the values of the second and
subsequent elements of the list to the function message.

As we have seen, message is an Emacs Lisp function especially
designed for sending a one line message to a user. (See The message function.) In summary, the message
function prints its first argument in the echo area as is, except for
occurrences of ‘%d’ or ‘%s’ (and various other %-sequences
which we have not mentioned). When it sees a control sequence, the
function looks to the second or subsequent arguments and prints the
value of the argument in the location in the string where the control
sequence is located.

In the interactive multiply-by-seven function, the control string
is ‘%d’, which requires a number, and the value returned by
evaluating (* 7 5) is the number 35. Consequently, the number 35
is printed in place of the ‘%d’ and the message is ‘The result
is 35’.

(Note that when you call the function multiply-by-seven, the
message is printed without quotes, but when you call message, the
text is printed in double quotes. This is because the value returned by
message is what appears in the echo area when you evaluate an
expression whose first element is message; but when embedded in a
function, message prints the text as a side effect without
quotes.)